129 lines
3.4 KiB
Python
129 lines
3.4 KiB
Python
#
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# Image to graph utility
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#
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# For the given data we have:
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# dip_hw_3.mat["d1a"] # [MN x MN] affinity matrix
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# dip_hw_3.mat["d2a"] # [M x N x 3] RGB image
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# dip_hw_3.mat["d2b"] # [M x N x 3] RGB image
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#
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#
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# author: Christos Choutouridis <cchoutou@ece.auth.gr>
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# date: 05/07/2025
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#
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try:
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import numpy as np
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from numpy._typing import NDArray
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from sklearn.metrics import pairwise_distances
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# Testing requirements
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import matplotlib.pyplot
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from scipy.io import loadmat
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except ImportError as e:
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print("Missing package: ", e)
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print("Run: pip install -r requirements.txt to install.")
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exit(1)
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def image_to_graph(
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img_array: NDArray[np.floating]
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) -> NDArray[np.float64]:
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"""
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Converts an input image into a fully connected graph represented
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by an affinity matrix.
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Parameters:
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----------
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img_array : np.ndarray of shape (M, N, C), dtype=float
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The input image with C channels (e.g., 3 for RGB),
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with values normalized in [0, 1].
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Returns:
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-------
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affinity_mat : np.ndarray of shape (M*N, M*N), dtype=float
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Symmetric affinity matrix representing the fully connected graph.
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A(i, j) = 1 / ||pixel_i - pixel_j||_2
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"""
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if not np.issubdtype(img_array.dtype, np.floating):
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raise ValueError("img_array must be of float type with values in [0, 1].")
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M, N, C = img_array.shape
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pixels = img_array.reshape(-1, C) # shape (M*N, C)
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# Compute Euclidean distances between all pixel vectors
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distances = pairwise_distances(pixels, metric='euclidean') # shape (MN, MN)
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# Avoid division by zero on the diagonal
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np.fill_diagonal(distances, 1e-10)
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# Affinity = 1 / e^d(i,j)
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affinity_mat = 1.0 / np.exp(distances)
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return affinity_mat
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def _test_1(plot : bool = False):
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"""
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Test image_to_graph() with a small 4x4 RGB random value array
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"""
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print(f" === Test 1 === ")
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print(f"")
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# Small 4x4 RGB with random values at [0, 1]
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img_array = np.random.rand(4, 4, 3).astype(np.float32)
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# affinity matrix calculation
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A = image_to_graph(img_array)
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# Print specs
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print("Shape of affinity matrix:", A.shape) # (16, 16)
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print("Is symmetric:", np.allclose(A, A.T)) # True
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print("Max value:", np.max(A))
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print("Min value:", np.min(A))
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if plot:
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matplotlib.use("TkAgg")
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matplotlib.pyplot.imshow(A, cmap='hot')
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matplotlib.pyplot.colorbar()
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matplotlib.pyplot.title("Affinity Matrix Heatmap")
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matplotlib.pyplot.show()
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def _test_2(plot : bool = False):
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"""
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Test image_to_graph() with d2b matrix
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"""
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print(f" === Test 2 === ")
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print(f"")
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data = loadmat("dip_hw_3.mat")
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img_array = data["d2b"] # shape (M, N, 3), dtype float, values in [0, 1]
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# Check shape and type
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print("Input image shape:", img_array.shape)
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print("dtype:", img_array.dtype)
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# affinity matrix calculation
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A = image_to_graph(img_array)
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# Print specs
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print("Affinity matrix shape:", A.shape)
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print("Is symmetric:", np.allclose(A, A.T))
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print("Max value:", np.max(A))
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print("Min value:", np.min(A))
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if plot:
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matplotlib.use("TkAgg")
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matplotlib.pyplot.imshow(A, cmap='hot')
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matplotlib.pyplot.title("Affinity Matrix Heatmap")
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matplotlib.pyplot.colorbar()
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matplotlib.pyplot.show()
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if __name__ == '__main__':
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# If you have TkAgg you can pass True, otherwise pass False
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_test_1(True)
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_test_2(True)
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